WOLCOTTVILLE, Ind.—R.D. Wolheter has gotten a stream of mailers from farm groups urging him to help pressure Congress to pass a farm bill. But as the agricultural sector remains strong, the grower of corn and soybeans on 3,000 acres in northeast Indiana has let them stack up on his desk.

For decades, the farm bill has served as the main vehicle for U.S. agriculture policy, getting renewed about every five years to keep billions of dollars flowing to farm subsidies and rural development programs. But lobbyists and lawmakers...